Fano 4-folds with nef tangent bundle in positive characteristic

Abstract

In characteristic 0, the Campana-Peternell conjecture claims thatthe only smooth Fano variety with nef tangent bundle should be homogeneous.In this paper, we study the positive characteristic version of the CampanaPeternell conjecture. In particular, we give an affirmative answer for Fano4-folds with nef tangent bundle and Picard number greater than one